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Testing Statistical Laws in Complex Systems

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Physical Review Letters 2019年第16期122卷 168301-168301页

作者： Martin Gerlach Eduardo G. Altmann Department of Chemical and Biological Engineering Northwestern University Evanston Illinois 60208 USA School of Mathematics and Statistics University of Sydney 2006 NSW Australia

The availability of large datasets requires an improved view on statistical laws in complex systems, such as Zipf’s law of word frequencies, the Gutenberg-Richter law of earthquake magnitudes, or scale-free degree distribution in networks. In this Letter, we discuss how the statistical analysis of these laws are affected by correlations present in the observations, the typical scenario for data from complex systems. We first show how standard maximum-likelihood recipes lead to false rejections of statistical laws in the presence of correlations. We then propose a conservative method (based on shuffling and undersampling the data) to test statistical laws and find that accounting for correlations leads to smaller rejection rates and larger confidence intervals on estimated parameters.

关键词： Preferential attachment Scaling laws of complex systems Stochastic processes & statistics Time series analysis

Strictly ( Q , S , R ) -dissipativity and exponential stability for switched systems with a dynamic event-triggered mechanism

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Journal of the Franklin Institute 2025年第11期362卷

作者： Wenqin Wang Wenhui Jia Jun Cheng Kaibo Shi Feng Liu School of Mathematical Sciences Tiangong University Tianjin 300387 PR China School of Mathematics and Statistics Guangxi Normal University Guilin Guangxi 541006 PR China School of Information Science and Engineering Chengdu University Chengdu 610106 Sichuan PR China Department of Radiology and Tianjin Key Laboratory of Functional Imaging Tianjin Medical University General Hospital Tianjin 300052 PR China

In order to enhance system efficiency and adaptability, this study investigates switched nonlinear systems with time-varying delay via a novel dynamic event-triggering mechanism incorporating a state-dependent threshold. With the goal to achieve strictly ( Q , S , R ) -dissipativity and exponential stability, a minimum LKF switching rule and a combination of multiple Lyapunov function approaches are adopted. The LKF contains not only the information of states and their derivatives, but also the related single integral and double integral information. Besides, to decouple coupling terms in the controller gain matrix, a more simple method is employed by introduced an additional external matrix, rather than the left–right multiplication approach used in the traditional way. Lastly, the numerical examples verify the efficacy of the suggested approaches.

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Role of ternary hybrid nanoparticle and EMHD on boundary layer flow with stretching-shrinking plate: Optimization analyses using RMS

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Results in Physics 2025年 74卷

作者： Ibrahim Mahariq Rania Saadeh Farhan Lafta Rashid Ahmad Qazza Hamiden Abd El-Wahed Khalifa Mohamed Kezzar Haifa Alqahtani Mohamed Rafik Sari College of Engineering and Architecture Gulf University for Science and Technology Mishref Kuwait Najjad Zeenni Faculty of Engineering Al Quds University Jerusalem Palestine University College Korea University Seoul 02481 South Korea Department of Medical Research China Medical University Hospital China Medical University Taichung Taiwan Department of Mathematics Faculty of Science Zarqa University Zarqa 13110 Jordan Petroleum Engineering Department College of Engineering University of Kerbala Karbala 56001 Iraq Department of Mathematics College of Science Qassim University Buraydah 51452 Saudi Arabia Materials and Energy Engineering Laboratory (LMGE) Technology Department Faculty of Technology 20 Aout 1955 University of Skikda PO Box 26 21000 Skikda Algeria Department of Statistics and Business Analytics United Arab Emirates University Al Ain 15551 Abu Dhabi United Arab Emirates Mechanics of Materials and Plant Maintenance Research Laboratory (LR3MI) Mechanical Engineering Department Faculty of Engineering University of Annaba BadjiMokhtar (UBMA) PO Box 12 23052 Annaba Algeria

In this present work the statistical and numerical analysis to optimizing the role of ternary hybrid nanoparticle (THNP) (i.e. T i - S W C N T - M W C N T ) on heat transfer of electromagnetohydrodynamic (EMHD) boundary layer flow with different effects (i.e. magnetic and electrical fields, stretching/shrinking and radiation source). The partial differential equations (PDEs) are transformed into model is simplified nonlinear ordinary differential equations using similarity transformation. The ordinary differential equations (ODEs) was numerically using the Runge-Kutta-Fehlberg method and the statistically analysis using the correlation analysis, probable error estimation, Regression, analysis of variance (ANOVA) and Response Surface Designs ( L 15 ). The findings are the optimization the role of THNP in both the local Nusselt number (Nu) and Skin friction coefficient ( C f ) impacted by the pertinent dimensionless characteristics for the considered flow case using RMS method. From the results, the volume fractions of 4% for both Ti, SWCNT, and MWCNT improve both thermal and fluidic properties of the nanofluid and show a combined effect of the nanoparticles. This study is marked by a significant decrease in the C f which implies a better flow characteristics for the hybrid nanoparticles case. Optimum conditions were achieved in the maximum value of the N u thus depicting high thermal enhancement and an enhanced cooling capability, which is very essential in thermal management systems.

关键词： Statistical Optimizing EMHD Stretching/shrinking Ternary hybrid Correlation Regression ANOVA RMS method Numerical method

Modified multiplicative decomposition model for tissue growth: Beyond the initial stress-free state

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arXiv 2020年

作者： Du, Yangkun Lü, Chaofeng Chen, Weiqiu Destrade, Michel Department of Engineering Mechanics Zhejiang University Hangzhou310027 China Department of Civil Engineering Zhejiang University Hangzhou310058 China Key Lab of Soft Machines and Smart Devices of Zhejiang Province Zhejiang University Hangzhou310027 China Soft Matter Research Center Zhejiang University Hangzhou310027 China School of Mathematics Statistics and Applied Mathematics NUI Galway University Road Galway Ireland

The multiplicative decomposition model is widely employed for predicting residual stresses and morphologies of biological tissues due to growth. However, it relies on the assumption that the tissue is initially in a stress-free state, which conflicts with the observations that any growth state of a biological tissue is under a significant level of residual stresses that helps to maintain its ideal mechanical conditions. Here, we propose a modified multiplicative decomposition model in which the initial state (or reference configuration) of a biological tissue is endowed with a residual stress instead of being stress-free. Releasing theoretically the initial residual stress, the initially stressed state is first transmitted into a virtual stress-free state, thus resulting in an initial elastic deformation. The initial virtual stress-free state subsequently grows to another counterpart with a growth deformation, and the latter is further integrated into its natural configuration of a real tissue with an excessive elastic deformation that ensures tissue compatibility. With this decomposition, the total deformation arising during growth may be expressed as the product of elastic deformation, growth deformation and initial elastic deformation, while the corresponding free energy density should depend on the initial residual stress and the total deformation. Three key issues including the explicit expression of the free energy density, the predetermination of the initial elastic deformation, and the initial residual stress are addressed. Finally, we consider a tubular organ as a representative example to demonstrate the effects of the proposed initial residual stress on stress distribution and on shape formation through an incremental stability analysis. Our results suggest that the initial residual stress exerts a major influence on the growth stress and the morphology of biological tissues. The model bridges the gap between any two growth states of a biological tissue t

关键词： Morphology

Mini-batch metropolis-hastings MCMC with reversible SGLD proposal

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arXiv 2019年

作者： Wu, Tung-Yu Rachel Wang, Y.X. Wong, Wing H. Institute for Computational and Mathematical Engineering Stanford University School of Mathematics and Statistics University of Sydney Department of Statistics Stanford University

Traditional MCMC algorithms are computationally intensive and do not scale well to large data. In particular, the Metropolis-Hastings (MH) algorithm requires passing over the entire dataset to evaluate the likelihood ratio in each iteration. We propose a general framework for performing MH-MCMC using mini-batches of the whole dataset and show that this gives rise to approximately a tempered stationary distribution. We prove that the algorithm preserves the modes of the original target distribution and derive an error bound on the approximation with mild assumptions on the likelihood. To further extend the utility of the algorithm to high dimensional settings, we construct a proposal with forward and reverse moves using stochastic gradient and show that the construction leads to reasonable acceptance probabilities. We demonstrate the performance of our algorithm in both low dimensional models and high dimensional neural network applications. Particularly in the latter case, compared to popular optimization methods, our method is more robust to the choice of learning rate and improves testing accuracy. Copyright © 2019, The Authors. All rights reserved.

关键词： Stochastic systems

Probabilistic methods for approximate archetypal analysis

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arXiv 2021年

作者： Han, Ruijian Osting, Braxton Wang, Dong Xu, Yiming Department of Statistics The Chinese University of Hong Kong Hong Kong Department of Mathematics University of Utah Salt Lake City United States School of Science and Engineering The Chinese University of Hong Kong Shenzhen China Guangdong Provincial Key Laboratory of Big Data Computing The Chinese University of Hong Kong Shenzhen China Scientific Computing and Imaging Institute University of Utah Salt Lake City United States

Archetypal analysis is an unsupervised learning method for exploratory data analysis. One major challenge that limits the applicability of archetypal analysis in practice is the inherent computational complexity of the existing algorithms. In this paper, we provide a novel approximation approach to partially address this issue. Utilizing probabilistic ideas from high-dimensional geometry, we introduce two preprocessing techniques to reduce the dimension and representation cardinality of the data, respectively. We prove that provided the data is approximately embedded in a low-dimensional linear subspace and the convex hull of the corresponding representations is well approximated by a polytope with a few vertices, our method can effectively reduce the scaling of archetypal analysis. Moreover, the solution of the reduced problem is near-optimal in terms of prediction errors. Our approach can be combined with other acceleration techniques to further mitigate the intrinsic complexity of archetypal analysis. We demonstrate the usefulness of our results by applying our method to summarize several moderately large-scale datasets. Copyright © 2021, The Authors. All rights reserved.

关键词： Large dataset

Four principles for improved statistical ecology

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arXiv 2023年

作者： Popovic, Gordana Mason, Tanya J. Marques, Tiago A. Potts, Joanne Drobniak, Szymon M. Joo, Rocío Altwegg, Res Burns, Carolyn C.I. McCarthy, Michael A. Johnston, Alison Nakagawa, Shinichi McMillan, Louise Devarajan, Kadambari Taggart, Patrick L. Wunderlich, Alison C. Mair, Magdalena M. Martínez-Lanfranco, Juan Andrés Lagisz, Malgorzata Pottier, Patrice P. Stats Central Mark Wainwright Analytical Centre UNSW Sydney Australia Centre for Ecosystem Science School of Biological Earth and Environmental Sciences UNSW Sydney Australia Centre for Research into Ecological and Environmental Modelling The Observatory University of St Andrews St Andrews United Kingdom Centro de Estatística e Aplicações Departamento de Biologia Animal Faculdade de Ciências da Universidade de Lisboa Portugal The Analytical Edge Statistical Consulting PO Box 47 Blackmans BayTAS Australia Evolution and Ecology Research Centre School of Biological Earth and Environmental Science University of New South Wales Sydney Australia Institute of Environmental Sciences Jagiellonian University Krakow Poland Global Fishing Watch WashingtonDC20036 United States Centre for Statistics in Ecology Environment and Conservation Department of Statistical Sciences University of Cape Town Rondebosch7701 South Africa Sydney Australia School of Ecosystem and Forest Sciences The University of Melbourne ParkvilleVIC Australia Centre for Research into Ecological and Environmental Modelling Mathematics and Statistics University of St Andrews St Andrews United Kingdom School of Mathematics and Statistics Victoria University of Wellington Wellington New Zealand Organismic and Evolutionary Biology Graduate Program University of Massachusetts at Amherst AmherstMA United States Department of Natural Resources Science University of Rhode Island KingstonRI United States Vertebrate Pest Research Unit Department of Primary Industries NSW QueanbeyanNSW Australia Institute of Biosciences São Paulo State University Coastal Campus São Vicente São Paulo Brazil Statistical Ecotoxicology University of Bayreuth Bayreuth Germany Theoretical Ecology University of Regensburg Regensburg Germany Department of Biological Sciences University of Alberta EdmontonAB Canada

Increasing attention has been drawn to the misuse of statistical methods over recent years, with particular concern about the prevalence of practices such as poor experimental design, cherry-picking and inadequate reporting. These failures are largely unintentional and no more common in ecology than in other scientific disciplines, with many of them easily remedied given the right guidance. Originating from a discussion at the 2020 International Statistical Ecology Conference, we show how ecologists can build their research following four guiding principles for impactful statistical research practices: 1. Define a focused research question, then plan sampling and analysis to answer it;2. Develop a model that accounts for the distribution and dependence of your data;3. Emphasise effect sizes to replace statistical significance with ecological relevance;4. Report your methods and findings in sufficient detail so that your research is valid and reproducible. Listed in approximate order of importance, these principles provide a framework for experimental design and reporting that guards against unsound practices. Starting with a well-defined research question allows researchers to create an efficient study to answer it, and guards against poor research practices that lead to false positives and poor replicability. Correct and appropriate statistical models give sound conclusions, good reporting practices and a focus on ecological relevance make results impactful and replicable. Illustrated with an example from a recent study into the impact of disturbance on upland swamps, this paper explains the rationale for the selection and use of effective statistical practices and provides practical guidance for ecologists seeking to improve their use of statistical methods. © 2023, CC BY-NC-ND.

关键词： Ecology

The Role of Agricultural Extension in Decentralizing the Sensitivity of Vegetable Farmers to the Risk of Residual Pesticide Effects

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Agricultural Sciences 2020年第8期11卷 722-729页

作者： Aiman Hamad Eltyeb Elshifa Ali Mergani Omeima Bashir Khalid Tawheed Mohammed Elheesin Shareef Khalid Ahmed Abbakar Department of Economic Agricultural and Rural Development Faculty of Agricultural and Environmental Sciences University of Gadarif Gadarif Sudan Department of Agricultural Extension and Rural Development College of Agricultural Studies Sudan University of Science and Technology Khartoum North Sudan Gansu Academy of Agricultural Sciences Lanzhou China Department of Agriculture Engineering Faculty of Agriculture University of Khartoum Khartoum Sudan Department of Mathematics and Physics Faculty of Education University of Gadarif Gadarif Sudan College of Mathematics and Statistics Northwest Normal University Lanzhou China

This study was carried out in the northern Khartoum (Bahry Locality) with the aim of knowing the role of agricultural extension in developing the awareness of the farmer to the danger of residual effect of pesticides (vegetable farmers). The social survey method was used to conduct this study;100 vegetable farmers were selected randomly. The data collected through questionnaires, observation, and interviews for primary data, previously concerned, and reference documents were used to collect secondary data. Data collected were analyzed using the statistical packages for social science (SPSS). The study yielded some useful results, the most important of which are: the presence of respondents who obtain their information about pesticides from merchants, the absence of a guide provider in their area, and the absence of any seminars or lectures on the use of pesticides, or programs. For example, radio and television programs were presented but protective clothing was not used. This study is based on the researcher's advocate for the following: intensifying agricultural extension and employee visits to the agricultural field, in addition to intensifying educational evidence for consumers regarding pesticides and providing preliminary data on pesticides and how to deal with them and increase them. Educate farmers about the safe use of pesticides and identify the risks and damages that pesticides cause to humans.

关键词： Agricultural Sector Pesticides Vegetables Awareness

Optimal Extensions of Resource Measures and their Applications

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arXiv 2020年

作者： Gour, Gilad Tomamichel, Marco Department of Mathematics and Statistics Institute for Quantum Science and Technology University of Calgary ABT2N 1N4 Canada Department of Electrical and Computer Engineering and Centre for Quantum Technologies National University of Singapore Singapore

We develop a framework to extend resource measures from one domain to a larger one. We find that all extensions of resource measures are bounded between two quantities that we call the maximal and minimal extensions. As an application to the framework, we show that any relative entropy (i.e. an additive function on pairs of quantum states that satisfies the data processing inequality) must be bounded by the min and max relative entropies. Along the way we use the framework to prove optimality properties of the generalized trace distance, the generalized fidelity, and the purified distance. As an application of the framework to entanglement theory we introduce a new technique to extend pure state entanglement measures to mixed bipartite states. Copyright © 2020, The Authors. All rights reserved.

关键词： Quantum entanglement